Her resignation means the Greens will be down two votes in the Senate for now.

It could possibly make it easier for the Turnbull Government to pass its legislation.

The dramatic move follows her fellow co-deputy leader Scott Ludlam's resignation after it was revealed he held dual Australian-NZ citizenship.

Senator Waters said her parents told her she had until age 21 to actively seek Canadian citizenship.

"At 21, I chose not to seek dual citizenship, and I have never even visited Canada since leaving at 11 months old," she said.

"However, after Scott's shock discovery, I immediately sought legal advice, and was devastated to learn that because of 70-year-old Canadian laws I had been a dual citizen from birth, and that Canadian law changed a week after I was born and required me to have actively renounce Canadian citizenship."

Senator Waters had not renounced her citizenship because she was unaware she was a dual citizen.

"Obviously, this is something that I should have sought advice on when I first nominated for the Senate in 2007, and I take full responsibility for this grave mistake and oversight. I am deeply sorry for the impact that it will have."

Senator Waters recently made world headlines as the first MP to make use of new laws allowing breastfeeding in the Parliament, garnering a positive reaction from none other than Snoop Dogg.

Greens Senator Larissa Waters and her baby in Senate Chamber at Parliament House in Canberra. Picture Kym Smith

The 40-year-old Brisbane-based senator was elected in 2010 and began her Senate service in 2011.

Mr Ludlam announced his resignation from federal parliament after finding out he was improperly elected more than a decade ago.

Mr Ludlam said it was recently brought to his attention that he holds dual citizenship of Australia and New Zealand.'

Under section 44 of the constitution, that makes him ineligible to hold elected office.

Senator Ludlam labelled it a "ridiculous oversight".

"I apologise unreservedly for this mistake," he said in a statement on Friday last week.

"This was my error, something I should have checked when I first nominated for preselection in 2006."

Instead of going through protracted legal proceedings, he resigned as a senator for Western Australia and co-deputy leader of the Australian Greens.

Greens co-deputy Scott Ludlam resigns

Senator Ludlam was born in Palmerston North in New Zealand and left the country with his family when he was three.

He settled in Australia not long before his ninth birthday, before being naturalised when he was in his mid-teens.

"(I) assumed that was the end of my New Zealand citizenship."

"It is entirely my responsibility - it wasn't the way I was hoping to go out."